Linear and Nonlinear Dynamical Systems Data Analytic Techniques and an Application to Developmental Data PDF Download

Author: Steven Marshall Boker
Publisher:
ISBN:
Category :
Languages : en
Pages : 268

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Author: Steven M Boker
Publisher: Psychology Press
ISBN: 1135611548
Category : Medical
Languages : en
Pages : 293

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Book Description
Each volume in the Notre Dame Series on Quantitative Methodology features leading methodologists and substantive experts who provide instruction on innovative techniques designed to enhance quantitative skills in a substantive area. This latest volume focuses on the methodological issues and analyses pertinent to understanding psychological data from a dynamical system perspective. Dynamical systems analysis (DSA) is increasingly used to demonstrate time-dependent variable change. It is used more and more to analyze a variety of psychological phenomena such as relationships, development and aging, emotional regulation, and perceptual processes. The book opens with the best occasions for using DSA methods. The final two chapters focus on the application of dynamical systems methods to problems in psychology such as substance use and gestural dynamics. In addition, it reviews how and when to use: time series models from a discrete time perspective stochastic differential equations in continuous time estimating continuous time differential equation models multilevel models of differential equations to estimate within-person dynamics and the corresponding population means new SEM models for dynamical systems data Data Analytic Techniques for Dynamical Systems is beneficial to advanced students and researchers in the areas of developmental psychology, family studies, language processes, cognitive neuroscience, social and personality psychology, medicine, and emotion. Due to the book’s instructive nature, it serves as an excellent text for advanced courses on this particular technique.

Author: Stephen J. Guastello
Publisher: CRC Press
ISBN: 1439820023
Category : Mathematics
Languages : en
Pages : 616

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Book Description
Although its roots can be traced to the 19th century, progress in the study of nonlinear dynamical systems has taken off in the last 30 years. While pertinent source material exists, it is strewn about the literature in mathematics, physics, biology, economics, and psychology at varying levels of accessibility. A compendium research methods reflect

Author: Karl M. Newell
Publisher: Psychology Press
ISBN: 1317779126
Category : Psychology
Languages : en
Pages : 330

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Book Description
There has been an increasing interest in the application of dynamical systems to the study of development over the last decade. The explosion of the dynamical systems framework in the physical and biological sciences has opened the door to a new Zeitgeist for studying development. This appeal to dynamical systems by developmentalists is natural given the intuitive links between the established fundamental problems of development and the conceptual and operational scope of nonlinear dynamical systems. This promise of a new approach and framework within which to study development has led to some progress in recent years but also a growing appreciation of the difficulty of both fully examining the new metaphor and realizing its potential. Divided into 4 parts, this book is a result of a recent conference on dynamical systems and development held at Pennsylvania State University. The first 3 parts focus on the content domains of development that have given most theoretical and empirical attention to the potential applications of dynamical systems--physical growth and movement, cognition, and communication. These parts show that a range of nonlinear models have been applied to a host of developmental phenomena. Part 4 highlights two particular methodological issues that hold important implications for the modeling of developmental phenomena with dynamical systems techniques.

Author: Alexander G. Ramm
Publisher: John Wiley & Sons
ISBN: 111819960X
Category : Mathematics
Languages : en
Pages : 522

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Book Description
Demonstrates the application of DSM to solve a broad range of operator equations The dynamical systems method (DSM) is a powerful computational method for solving operator equations. With this book as their guide, readers will master the application of DSM to solve a variety of linear and nonlinear problems as well as ill-posed and well-posed problems. The authors offer a clear, step-by-step, systematic development of DSM that enables readers to grasp the method's underlying logic and its numerous applications. Dynamical Systems Method and Applications begins with a general introduction and then sets forth the scope of DSM in Part One. Part Two introduces the discrepancy principle, and Part Three offers examples of numerical applications of DSM to solve a broad range of problems in science and engineering. Additional featured topics include: General nonlinear operator equations Operators satisfying a spectral assumption Newton-type methods without inversion of the derivative Numerical problems arising in applications Stable numerical differentiation Stable solution to ill-conditioned linear algebraic systems Throughout the chapters, the authors employ the use of figures and tables to help readers grasp and apply new concepts. Numerical examples offer original theoretical results based on the solution of practical problems involving ill-conditioned linear algebraic systems, and stable differentiation of noisy data. Written by internationally recognized authorities on the topic, Dynamical Systems Method and Applications is an excellent book for courses on numerical analysis, dynamical systems, operator theory, and applied mathematics at the graduate level. The book also serves as a valuable resource for professionals in the fields of mathematics, physics, and engineering.

Author: Richard A. Heath
Publisher: Psychology Press
ISBN: 1135670544
Category : Psychology
Languages : en
Pages : 410

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Book Description
Additional Resource Materials Human behavior would not be interesting to us if it remained the same from one moment to the next. Moreover, we tend to be sensitive to changes in people's behavior, especially when such change impacts on our own, and other's, behavior. This book describes a variety of techniques for investigating change in behavior. It employs conventional time series methods, as well as recently developed methodology using nonlinear dynamics, including chaos, a term that is not easy to define, nor to confirm. Although nonlinear methods are being used more frequently in psychology, a comprehensive coverage of methods, theory and applications, with a particular focus on human behavior, is needed. Between these covers, the reader is led through various procedures for linear and nonlinear time series analysis, including some novel procedures that allow subtle temporal aspects of human cognition to be detected. Analyses of reaction times, heart-rate, psychomotor skill, decision making, and EEG are supplemented by a contemporary review of recent dynamical research in developmental psychology, psychopathology, and human cognitive processes. A consideration of nonlinear dynamics assists our understanding of deep issues such as: Why is our short-term memory capacity limited? Why do chronic disorders, and also cognitive development, progress through stage-like transitions? Why do people make irrational decisions? This book will be of particular interest to researchers, practitioners, and advanced students in a variety of areas in psychology, particularly in human experimental and physiological psychology. Data analyses are performed using the latest nonlinear dynamics computer packages. A comprehensive WWW resource of software and supplementary information is provided to assist the reader's understanding of the novel, and potentially revolutionary, procedures described in the book.

Author: J. Nathan Kutz
Publisher: SIAM
ISBN: 161197450X
Category : Science
Languages : en
Pages : 241

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Book Description
Data-driven dynamical systems is a burgeoning field?it connects how measurements of nonlinear dynamical systems and/or complex systems can be used with well-established methods in dynamical systems theory. This is a critically important new direction because the governing equations of many problems under consideration by practitioners in various scientific fields are not typically known. Thus, using data alone to help derive, in an optimal sense, the best dynamical system representation of a given application allows for important new insights. The recently developed dynamic mode decomposition (DMD) is an innovative tool for integrating data with dynamical systems theory. The DMD has deep connections with traditional dynamical systems theory and many recent innovations in compressed sensing and machine learning. Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems, the first book to address the DMD algorithm, presents a pedagogical and comprehensive approach to all aspects of DMD currently developed or under development; blends theoretical development, example codes, and applications to showcase the theory and its many innovations and uses; highlights the numerous innovations around the DMD algorithm and demonstrates its efficacy using example problems from engineering and the physical and biological sciences; and provides extensive MATLAB code, data for intuitive examples of key methods, and graphical presentations.

Author: Jason T. Newsom
Publisher: Taylor & Francis
ISBN: 1000905977
Category : Psychology
Languages : en
Pages : 522

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Book Description
Longitudinal Structural Equation Modeling is a comprehensive resource that reviews structural equation modeling (SEM) strategies for longitudinal data to help readers determine which modeling options are available for which hypotheses. This accessibly written book explores a range of models, from basic to sophisticated, including the statistical and conceptual underpinnings that are the building blocks of the analyses. By exploring connections between models, it demonstrates how SEM is related to other longitudinal data techniques and shows when to choose one analysis over another. Newsom emphasizes concepts and practical guidance for applied research rather than focusing on mathematical proofs, and new terms are highlighted and defined in the glossary. Figures are included for every model along with detailed discussions of model specification and implementation issues and each chapter also includes examples of each model type, descriptions of model extensions, comment sections that provide practical guidance, and recommended readings. Expanded with new and updated material, this edition includes many recent developments, a new chapter on growth mixture modeling, and new examples. Ideal for graduate courses on longitudinal (data) analysis, advanced SEM, longitudinal SEM, and/or advanced data (quantitative) analysis taught in the behavioral, social, and health sciences, this new edition will continue to appeal to researchers in these fields.

Author: Rolf Isermann
Publisher: Springer Science & Business Media
ISBN: 3540788794
Category : Technology & Engineering
Languages : en
Pages : 705

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Book Description
Precise dynamic models of processes are required for many applications, ranging from control engineering to the natural sciences and economics. Frequently, such precise models cannot be derived using theoretical considerations alone. Therefore, they must be determined experimentally. This book treats the determination of dynamic models based on measurements taken at the process, which is known as system identification or process identification. Both offline and online methods are presented, i.e. methods that post-process the measured data as well as methods that provide models during the measurement. The book is theory-oriented and application-oriented and most methods covered have been used successfully in practical applications for many different processes. Illustrative examples in this book with real measured data range from hydraulic and electric actuators up to combustion engines. Real experimental data is also provided on the Springer webpage, allowing readers to gather their first experience with the methods presented in this book. Among others, the book covers the following subjects: determination of the non-parametric frequency response, (fast) Fourier transform, correlation analysis, parameter estimation with a focus on the method of Least Squares and modifications, identification of time-variant processes, identification in closed-loop, identification of continuous time processes, and subspace methods. Some methods for nonlinear system identification are also considered, such as the Extended Kalman filter and neural networks. The different methods are compared by using a real three-mass oscillator process, a model of a drive train. For many identification methods, hints for the practical implementation and application are provided. The book is intended to meet the needs of students and practicing engineers working in research and development, design and manufacturing.

Author: James Ramsay
Publisher: Springer
ISBN: 1493971905
Category : Mathematics
Languages : en
Pages : 242

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Book Description
This text focuses on the use of smoothing methods for developing and estimating differential equations following recent developments in functional data analysis and building on techniques described in Ramsay and Silverman (2005) Functional Data Analysis. The central concept of a dynamical system as a buffer that translates sudden changes in input into smooth controlled output responses has led to applications of previously analyzed data, opening up entirely new opportunities for dynamical systems. The technical level has been kept low so that those with little or no exposure to differential equations as modeling objects can be brought into this data analysis landscape. There are already many texts on the mathematical properties of ordinary differential equations, or dynamic models, and there is a large literature distributed over many fields on models for real world processes consisting of differential equations. However, a researcher interested in fitting such a model to data, or a statistician interested in the properties of differential equations estimated from data will find rather less to work with. This book fills that gap.